# Function to print upper half of diamond (pyramid)







def      _a					(   lowercase__	:      Tuple			):







     '''simple docstring'''


     for i in range(0  ,	lowercase__			):
          for _ in range(0  ,	n - i - 1			):  # printing spaces
               print(' '  ,	end=''			)
          for _ in range(0  ,	i + 1			):  # printing stars
               print('* '  ,	end=''			)
          print()







def      _a					(   lowercase__	:      List[str]			):







     '''simple docstring'''


     for i in range(lowercase__  ,	0  ,	-1			):
          for _ in range(lowercase__  ,	0  ,	-1			):  # printing stars
               print('* '  ,	end=''			)
          print()
          for _ in range(n - i + 1  ,	0  ,	-1			):  # printing spaces
               print(' '  ,	end=''			)







def      _a					(   lowercase__	:      int			):







     '''simple docstring'''


     if n <= 0:
          print('       ...       ....        nothing printing :('			)
          return
     floyd(lowercase__			)  # upper half
     reverse_floyd(lowercase__			)  # lower half


if __name__ == "__main__":
      print(r"| /\ | |- |  |-  |--| |\  /| |-")
      print(r"|/  \| |- |_ |_  |__| | \/ | |_")
      SCREAMING_SNAKE_CASE__		:       List[str]       						=       1
      while K:
            SCREAMING_SNAKE_CASE__		:       List[str]       						=       int(input("enter the number and , and see the magic : "))
            print()
            pretty_print(user_number)
            SCREAMING_SNAKE_CASE__		:       Any       						=       int(input("press 0 to exit... and 1 to continue..."))

      print("Good Bye...")




"""simple docstring"""


from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   List[Any]:




						'''simple docstring'''



						def is_in_circle(__lowerCAmelCase  ,       __lowerCAmelCase							) -> bool:
												lowerCamelCase__   =sqrt((x**2) + (y**2)							)
												# Our circle has a radius of 1, so a distance
												# greater than 1 would land outside the circle.
												return distance_from_centre <= 1

						# The proportion of guesses that landed in the circle
						lowerCamelCase__   =mean(
						    int(is_in_circle(uniform(-1.0  ,       1.0							)  ,       uniform(-1.0  ,       1.0							)							)							)
						    for _ in range(__lowerCAmelCase							)							)
						# The ratio of the area for circle to square is pi/4.
						lowerCamelCase__   =proportion * 4
						print(F'''The estimated value of pi is {pi_estimate}'''							)
						print(F'''The numpy value of pi is {pi}'''							)
						print(F'''The total error is {abs(pi - pi_estimate							)}'''							)





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase = 0.0  ,       __lowerCAmelCase = 1.0  ,       )				->   float:




						'''simple docstring'''



						return mean(
						    function_to_integrate(uniform(__lowerCAmelCase  ,       __lowerCAmelCase							)							) for _ in range(__lowerCAmelCase							)							) * (max_value - min_value)





def      lowerCamelCase_					(   __lowerCAmelCase  ,       __lowerCAmelCase = 0.0  ,       __lowerCAmelCase = 1.0							)				->   None:




						'''simple docstring'''



						def identity_function(__lowerCAmelCase							) -> float:
												return x

						lowerCamelCase__   =area_under_curve_estimator(
						    __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase  ,       __lowerCAmelCase							)
						lowerCamelCase__   =(max_value * max_value - min_value * min_value) / 2

						print("******************"							)
						print(F'''Estimating area under y=x where x varies from {min_value} to {max_value}'''							)
						print(F'''Estimated value is {estimated_value}'''							)
						print(F'''Expected value is {expected_value}'''							)
						print(F'''Total error is {abs(estimated_value - expected_value							)}'''							)
						print("******************"							)





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   None:




						'''simple docstring'''



						def function_to_integrate(__lowerCAmelCase							) -> float:
												return sqrt(4.0 - x * x							)

						lowerCamelCase__   =area_under_curve_estimator(
						    __lowerCAmelCase  ,       __lowerCAmelCase  ,       0.0  ,       2.0							)

						print("******************"							)
						print("Estimating pi using area_under_curve_estimator"							)
						print(F'''Estimated value is {estimated_value}'''							)
						print(F'''Expected value is {pi}'''							)
						print(F'''Total error is {abs(estimated_value - pi							)}'''							)
						print("******************"							)


if __name__ == "__main__":
	import doctest

	doctest.testmod()


